Descriptions

This thesis presents a model of legged locomotion in
which position and velocity of body are directly controlled
by positions and velocities of feet. One central
relationship between foot acceleration, leg stroke and body
velocity is developed. Procedures for determining all
parameters of a step sequence including periods of constant
body velocity (steady state) and constant linear acceleration
of body (transient state) are presented.
The following assumptions are used. Symmetrical
trapezoidal velocity profiles are used for body and feet.
Transient period is longer than or equal to one step time and
a multiple of half step time. Step time and duty factor are
constant during each locomotion stage. Stepping movements of
a pair of legs are 180° out of phase and successive prints of
one foot are symmetrically placed relative to the other foot.
Starting and stopping occur with feet on a line perpendicular
to the direction of body motion. Locomotion starts by
lifting one foot and ends with one foot on the ground and the
other being placed.
When analyzing walking, designing a walking machine or
designing a stepping sequence for an existing walking
machine, it is important to understand constraints placed on
body motion by motion of a single leg. Two dimensionless
numbers which describe foot velocity profile are developed.
Two additional dimensionless numbers result from constraint
of leg workspace by foot acceleration and body velocity
during steady state. These numbers provide useful
relationships for design procedures.
Defining a walking sequence requires transformation of
objectives from global to body coordinates and continuously
accounting for the relationship between these two systems.
The technique described does this when body acceleration is
non-zero as well as when body velocity is constant.
Relationship between body and global coordinates is tracked
for one leg pair using two diagrams: 1) position of feet
relative to body versus time; 2) distances moved by feet and
body in the global frame.
A closed form inverse kinematic solution and an
algorithm to find workspace for general three-revolute
manipulator are presented.